Lecture Discrete Mathematics given by Prof. Dr. Sebastian Iwanowski

German website

study programs: Bachelor of Computer Science (B_Inf), Computer Engineering (B_Tinf), IT Engineering (B_ITE), Media Computer Science (B_Minf), Computer Games Technology (B_CGT), Business and Computer Science (B_Winf), e-Commerce (B_ECom), Smart Technology (B_STec), IT-Management Consulting & Auditing (B_IMCA), 1st semester

ECTS credits: 5

lecture term: summer and winter semester

prerequesites: precalculus mathematics of secondary school

language: This lecture is given in German in both semesters and in English in winter semester only.

schedule for WS 2017/18:

Wed, 14:00, HS 2 + Th, 17:00, HS 3

Tutorial: Wed, 12:30, HS 2

focus of this lecture

This lecture gives the mathematical fundamentals for further study in all IT related programs. The contents are highly related to a lot of parallel and subsequent courses. This lecture does not require any knowledge of programming.

This lecture covers standard material such as logics and proof concepts, set theory, number theory, combinatorics, and graph theory. Furthermore, we give an introduction in group and field theory which highlights in the construction algorithm for arbitrary finite fields. For exercises, some construction programs implemented by students of FH Wedel in a software project may be downloaded here  (instructions in German).

This lecture is complemented by exercises lead by teaching assistants.

content of teaching

The following links show the slides and the assignments of the course held in WS 2016/17. Updates in WS 2017/18 may occur continuously and will be indicated by a red update information. Students enrolled at FH Wedel will find all assignments and some student solutions on the handout server.

 1. Fundamentals of mathematics (updated on October 18, 2017)
    1.1 Motivation
    1.2 Propositional logic (Proof of Modus Tollens)
    1.3 Predicate logic

Assignment 01 (to be solved until October 25)

2. Set theory
    2.1 Basics
    2.2 Relations (Two-grade-example)
    2.3 Functions
    2.4 Boolean algebras

3. Proof concepts
    3.1 Glossary of mathematical structures
    3.2 Mathematical induction (3-divisabilitygrammar example)
    3.3 Other proof strategies

4. Number theory
    4.1 Divisibility
    4.2 Dividing with remainders
    4.3 Prime numbers
    4.4 Modular arithmetic

(Examples for gcd and lcm, PrimeFactorisation with Maxima)
Note for the factorisation file: You must store this with the extension .wxm (not .txt). This file can the be executed and altered by the open-source tool Maxima (download here for all operating systems or here an older but still functioning version on the handout server for Windows). Warning: The file should not be altered by any editor other tha Maxima's!

5. Algebraic structures
    5.1 Groups
    5.2 Fields

6. Combinatorics
    6.1 Enumeration formulae for sets
    6.2 Permutations

7. Graph theory
    7.1 Terminology und representation
    7.2 Path problems in graphs (including Dijkstra's algorithm) (graph examplesalgorithm example for Dijkstra)
    7.3 Trees (including Kruskal's algorithm) (Ddodecaeder graph as an example for Kruskal (red) and Dijkstra (blue))
    7.4 Planar graphs (Example for graph containing a subdivision of C3,3)
    7.5 Graph colouring

references

text book (in German)

Sebastian Iwanowski / Rainer Lang: Diskrete Mathematik mit Grundlagen, Springer 2014, ISBN 978-3-658-07130-1 (Print), 978-3-658-07131-8 (Online)

English books with partial coverage of this lecture (see slide references) or for further concentration:

Norman L. Biggs: Discrete Mathematics, Oxford University Press 2002 (2. edition), ISBN 0-19-850717-8
This book covers nearly all material of this lecture in a slightly more mathematical manner except for some graph algorithms. This book also covers a a lot of material not discussed in this lecture.

Neville Dean: The Essence of Discrete Mathematics, Prentice Hall 1997, ISBN 0-1334-5943-8
This book covers the first 2 chapters of this lecture entirely on a more elementary level.

Susanna S. Epp: Discrete Mathematics with Applications, Brooks/Cole 1995 (2. edition), ISBN 0-534-94446-9
This book covers most of this lecture (Chapter 5 not at all), some on a more elementary level, and lays a strong focus in algorithmic applications.

Jiri Matousek / Jaroslav Nesetril: An Invitation to Discrete Mathematics, Oxford University Press 2008 (2. edition), ISBN 0-1985-7042-2
This book covers some of the material of this lecture on a more scientific level and a lot of other issues for broadening the horizon. 

Kenneth H. Rosen: Discrete Mathematics and its Applications, McGraw-Hill 2003, ISBN 0-07-242434-6
This book covers a big part of this lecture.

literature for broadening the mathematical horizon:

Martin Aigner / Günter Ziegler: Proofs from THE BOOK, Springer-Verlag 2010 (4. edition), ISBN 978-3-642-00855-9
Martin Aigner is my teacher of Discrete Mathematics.

In WS 2016, proofs of this book are presented in my seminar.